Turbulent Flow Of Liquid Metal Research Articles

Measurements of the magnetic field induced by a turbulent flow of liquid metal

Initial results from the Madison Dynamo Experiment provide details of the inductive response of a turbulent flow of liquid sodium to an applied magnetic field. The magnetic field structure is reconstructed from both internal and external measurements. A mean toroidal magnetic field is induced by the flow when an axial field is applied, thereby demonstrating the omega effect. Poloidal magnetic flux is expelled from the fluid by the poloidal flow. Small-scale magnetic field structures are generated by turbulence in the flow. The resulting magnetic power spectrum exhibits a power-law scaling consistent with the equipartition of the magnetic field with a turbulent velocity field. The magnetic power spectrum has an apparent knee at the resistive dissipation scale. Large-scale eddies in the flow cause significant changes to the instantaneous flow profile resulting in intermittent bursts of nonaxisymmetric magnetic fields, demonstrating that the transition to a dynamo is not smooth for a turbulent flow.

Development of a Three Dimensional Mathematical Model of the Electromagnetic Casting of Steel.

The development of a mathematical model for the electromagnetic casting of steel is described. The model is three dimensional and computes the evolution of the electromagnetic field, the turbulent liquid metal flow and the free surface of the metal pool with time. This is achieved by simultaneous solution of the MHD form of Maxwell's equations, Ohm's law, the Navier–Stokes and continuity equations (by large eddy simulation) and an equation for the free surface. Solution is by a combination of finite element (field and flow equations) and finite difference (surface equation) methods on an Eulerian-Lagrangian grid. The model was first tested against measurements, by others, of magnetic fields and induced currents in an apparatus akin to an electromagnetic caster, and then against computations, performed using finite difference methods by other investigators, of laminar flow within a 2D rectangular cavity. The model was also tested against classical equations for the oscillations of a free surface in a rectangular trough and then against measurements, at Nippon Steel Corporation, of the surface oscillations of a mercury pool surrounded by an inductor carrying alternating current. Use of the model to predict the behavior of a steel caster is to be described in a subsequent paper.

Numerical analysis for laminar and turbulent liquid-metal flow in a transverse magnetic field

A numerical analysis was conducted for mercury and lithium MHD flows in rectangular channels under uniform transverse magnetic fields. In order to couple electromagnetic effects with hydrodynamics, the axial momentum equation and the equations for the axial induced magnetic field in the fluid and wall were solved simultaneously. The suppression of turbulence was taken into account by using the modified k - e model of turbulence. The analytical results agreed well with the experimental results for the velocity profiles in mercury flow and skin friction coefficients in mercury and lithium flows. The M-shaped velocity profile for lithium flows was found, which is expected to be one reason for heat transfer enhancement at the wall parallel to the magnetic field.

Numerical simulation of turbulent temperature fluctuations in liquid metals

The method of direct numerical simulation is used to investigate temperature fluctuations in fully developed turbulent liquid metal flows. Subgrid scale models using one transport equation account for the turbulence not resolved by the finite difference grid. A special subgrid scale heat flux model for liquid metal flows is deduced together with a method of calculating the model coefficients. At very small Peclet numbers the temperatures become independent of model parameters.Numerical results for the Nusselt number in plane channels and for radial temperature and eddy conductivity profiles in annuli agree with published data. Nusselt numbers determined numerically for annuli indicate that many empirical correlations overestimate the influence of the ratio of radii. The numerical results for the eddy conductivity profiles may be used to reduce these problems. The statistical properties of the temperature fluctuations simulated are within the scatter band of experimental data. The numerical results confirm Lawn's theory, giving reasonable heat flux correlation coefficients which depend only weakly on the problem marking parameters.

Heat transfer in turbulent liquid metal flow in channels with various wall conditions

Heat transfer in turbulent liquid metal flow in channels with various wall conditions

Axially varying heat flux effects in tubes, flat ducts and widely spaced rod bundles cooled by a turbulent flow of liquid metal

This paper presents accurate theoretical results on temperature distributions and heat transfer coefficients for steady turbulent flow of a liquid metal in channels with an arbitrary prescribed wall heat flux in the flow direction. The geometries considered are the circular tube, the infinite flat duct and the widely spaced rod bundle. A new mathematical method of solution is given which lies midway between the purely numerical and analytical methods.

Slug-Flow Nusselt Numbers for In-Line Flow Through Unbaffled Rod Bundles

A theoretical study of fully developed heat transfer for in-line slug flow through unbaffled equilateral triangular bundles is reported. Results are given for the pitch: diameter range 1.05 to 2.00. Two sets of thermal boundary conditions have been considered: (a) uniform wall heat flux in all directions and (b) uniform wall heat flux in the axial direction and uniform wall temperature in the circumferential direction. For the first set, results on the circumferential variation of the wall temperature are given; and for the second, those on the circumferential variation of the wall heat flux are given. For both sets, average Nusselt numbers and circumferential variations of the local heat-transfer coefficients are also given. In all cases, the results are presented in the form of convenient dimensionless groups, and it is shown that they apply to, or can be used for, the estimation of the same dependent variables for turbulent flow of liquid metals through rod bundles.It has also been shown that for the P/D ratios and Peclet numbers normally employed in liquid-metal-cooled reactor cores, the ratio of the maximum temperature variation around a rod to the average wall-to-bulk temperature drop, in the case of uniform wall heat flux in all directions, is not greatly different for both slug and turbulent flows.

Thermal Entry Length for Turbulent Flow of Liquid Metals in Pipes With Constant Wall Heat Flux

Thermal Entry Length for Turbulent Flow of Liquid Metals in Pipes With Constant Wall Heat Flux

Theoretical investigation of the effect of an internal heat source on turbulent liquid metal heat transfer in a channel with uniform heat flux

The effect of an internal heat source on the heat transfer characteristics for turbulent liquid metal flow between parallel plates is studied analytically. The analysis is carried out for the conditions of uniform internal heat generation, uniform wall heat flux, and fully established temperature and velocity profiles. Consideration is given both to the uniform or slug flow approximation and the power law approximation for the turbulent velocity profile. Allowance is made for turbulent eddying within the liquid metal through the use of an idealized eddy diffusivity function. It is found that the Nusselt number is unaffected by the heat source strength when the velocity profile is assumed to be uniform over the channel cross section. In the case of a 1/7-power velocity expression, the Nusselt numbers are lower than those in the absence of internal heat generation, and decrease with diminishing eddy conduction. Nusselt numbers, in the absence of an internal heat source, are compared with existing calculations, and indications are that the present results are adequate for preliminary design purposes.

Heat transfer in a region of thermal stabilization in the turbulent flow of liquid metals in a tube

In the work described here, local heat-transfer coefficients were determined for turbulent flows of liquid metals (Pr ≃ 0.02) in a region of thermal stabilization (ιt equal to 5, 10, 15 d) for Reynolds numbers Re = 104-2·105. The determinations were made by two methods: by the measurement and analysis of temperature profiles in the flow without taking into account the thermal contact resistance, and by directly measuring the temperature changes in the wall, taking into account the thermal contact resistance. Hydrodynamic stabilization of the flow was maintained during the experiments (ιt ≃30 d).

Unilateral Heat Transfer to Liquid Metals Flowing in Annuli

Using a Lyon (3) type of analysis, theoretical Nusselt numbers have been calculated for liquid metals flowing in concentric annuli, under conditions of constant heat flux and fully-established turbulent flow. These have been expressed in the form of semiempirical equations for the case of heat transfer from the inner wall only and for the case of heat transfer from the outer wall only. Predictions on the basis of these equations are compared with those by other relationships and with experimental results. The proposed equations are consistent with those for turbulent flow of liquid metals inside circular tubes and between parallel plates; the former being the limit for an annulus as r2/r1 approaches infinity, and the latter being the limit as r2/r1 approaches unity.

Heat-transfer from the turbulent flow of liquid metals in tubes

In this article, the results are given of investigations of heat-transfer for turbulent flow of alkali and heavy liquid metals in tubes. The heat-transfer coefficients were obtained by using two different methods: by the measurement of the temperature field in the flow of the liquid metal and calculating the coefficients, and by the measurement of the wall temperature and the mean liquid-metal temperature. A comparison of the results obtained by these methods leads to certain results concerning the magnitude of the thermal-contact resistance.

Investigation of heat transfer in the turbulent flow of liquid metals in tubes

Experiments were carried out on two different pieces of apparatus~ On one setup mercury was used, on the other lead and a eutectic lead--bismuth alloy (43.5%pb+ + 56, 5~ Bi). Experiments with Mercury. Before being put into the apparatus, P-3 type mercury (99.9% pure) was passed through a chamois filter. The experimental apparatus was a " tube-intube" type heat exchanger made from 1KhlSN9T steel. The mercury flowed inside a tube with diameter of 17 • 12.5 ram. The heat given off in the pump and loop was carried off from the mercury by water flowing in an annular space 4.5 mm wide. Heat exchange over a length of 760 mm between the mercury and water was realized on the counterflow principle, with the mercury moving from the bottom upward. Before entry into the working part of the tube, allowance w~as made for a hydrodynamic stabilization interval, equal to 40 diameters. To reduce heat losses over the parts of the tube prior to the heat exchanger" and after it, compensation heaters were mounted on those parts. The temperature of the heat-exchange surface between the mercury and water at the inlet and outlet were measured by thermocouples. The power of the heat exchanger was determined from the mass flow rate and cooling of the mercury and was controlled according to the mass flow rate and heating of the water. The arithmetic mean temperature, calculated from the readings of thermoeouples placed at the inlet and outlet of the heat exchanger, was assumed as the mean temperature of the mercury. The mean temperature of the heat-exchange surface was determined by planimetry of the temperature profile over the length of the heat exchanger, taking into account corrections for depth to which the thermocouples were built in.